N = 192
| group | gender | n | age_mean | age_sd | age_median | age_IQR |
|---|---|---|---|---|---|---|
| EX 50-50 | F | 38 | 19.132 | 1.711 | 18 | 1.75 |
| EX 50-50 | M | 25 | 20.320 | 3.198 | 19 | 3.00 |
| EX 80-20 | F | 38 | 19.447 | 3.644 | 18 | 1.75 |
| EX 80-20 | M | 28 | 19.607 | 2.347 | 19 | 2.00 |
| EX 20-80 | F | 39 | 20.179 | 4.667 | 19 | 2.00 |
| EX 20-80 | M | 24 | 19.375 | 1.952 | 19 | 2.00 |
N = 184
| group | gender | n | age_mean | age_sd | age_median | age_IQR |
|---|---|---|---|---|---|---|
| EX 50-50 | F | 36 | 19.194 | 1.737 | 18.5 | 2 |
| EX 50-50 | M | 22 | 20.318 | 3.272 | 19.0 | 3 |
| EX 80-20 | F | 37 | 19.378 | 3.669 | 18.0 | 1 |
| EX 80-20 | M | 27 | 19.519 | 2.343 | 19.0 | 2 |
| EX 20-80 | F | 39 | 20.179 | 4.667 | 19.0 | 2 |
| EX 20-80 | M | 23 | 19.435 | 1.973 | 19.0 | 2 |
| group | n | age_mean | age_sd | age_median | age_IQR |
|---|---|---|---|---|---|
| EX 50-50 | 58 | 19.621 | 2.470 | 19 | 2 |
| EX 80-20 | 64 | 19.438 | 3.157 | 19 | 2 |
| EX 20-80 | 62 | 19.903 | 3.887 | 19 | 2 |
Total number of catch trial exclusions = 8.
Catch trial exclusions were based on block 5 & 6 performance.
| Model | df | AIC | BIC | logLik | Test | L.Ratio | p.value | BF_10 | |
|---|---|---|---|---|---|---|---|---|---|
| base_mod | 1 | 4 | 226.496 | 242.128 | -109.248 | NA | NA | NA | |
| grp_mod | 2 | 6 | 228.323 | 251.772 | -108.162 | 1 vs 2 | 2.172 | 0.338 | 8.000000e-03 |
| value_mod | 3 | 7 | 176.484 | 203.840 | -81.242 | 2 vs 3 | 53.840 | 0.000 | 2.559852e+10 |
| grp_val | 4 | 9 | 179.296 | 214.469 | -80.648 | 3 vs 4 | 1.188 | 0.552 | 5.000000e-03 |
Main Effect of Group:
\(\chi^2(2) = 2.17, p = 0.338, BF_{10} < .01\)
Main Effect of Choice Value (i.e., Extreme Outcome effect):
\(\chi^2(1) = 53.84, p < .001, BF_{10} > 150\)
Interaction: Group \(\times\) Choice Value:
\(\chi^2(2) = 1.19, p = 0.552, BF_{10} < .01\)
| Value | Std.Error | DF | t-value | p-value | sig | r_effect | |
|---|---|---|---|---|---|---|---|
| (Intercept) | 0.413 | 0.034 | 181 | 12.219 | 0.000 | TRUE | 0.672 |
| group 8020_vs_50 | 0.041 | 0.047 | 181 | 0.872 | 0.384 | FALSE | 0.065 |
| group 2080_vs_50 | -0.026 | 0.047 | 181 | -0.552 | 0.581 | FALSE | 0.041 |
| choice_value1 | 0.102 | 0.024 | 181 | 4.336 | 0.000 | TRUE | 0.307 |
| group 8020_vs_50 :choice_value1 | -0.014 | 0.032 | 181 | -0.435 | 0.664 | FALSE | 0.032 |
| group 2080_vs_50 :choice_value1 | 0.020 | 0.033 | 181 | 0.620 | 0.536 | FALSE | 0.046 |
EX 80-20 vs. EX 50:
\(b = 0.04, t(181) = 0.87, p = 0.384, r = 0.06\)
EX 20-80 vs. EX 50:
\(b = -0.03, t(181) = -0.55, p = 0.581, r = 0.04\)
EX 80-20 vs. EX 50 | Choice Value (High vs. Low):
\(b = -0.01, t(181) = -0.43, p = 0.664, r = 0.03\)
EX 20-80 vs. EX 50 | Choice Value (High vs. Low):
\(b = 0.02, t(181) = 0.62, p = 0.536, r = 0.05\)
Note:
Proportions are taken within condition and context (High/Low). E.g., All the green bars in the top left sum to 1, all the orange bars in the top middle sum to 1, and so on.
Since non-numeric responses were permissible by the experiment’s program, data was filtered to remove all non-numeric inputs. If a participant’s inputs had a cumulative sum less than 20 or greater than 300, their results were removed. In total, 8 participants met this criteria.
| No | Yes | |
|---|---|---|
| EX 50-50 | 11 | 38 |
| EX 80-20 | 13 | 44 |
| EX 20-80 | 16 | 39 |
\(\chi^2(2) = 0.81, p = 0.667, \varphi_c = 0.07\)
| No | Yes | |
|---|---|---|
| EX 50-50 | -0.47 | 0.47 |
| EX 80-20 | -0.44 | 0.44 |
| EX 20-80 | 0.90 | -0.90 |
| No | Yes | |
|---|---|---|
| EX 50-50 | 0.642 | 0.642 |
| EX 80-20 | 0.658 | 0.658 |
| EX 20-80 | 0.369 | 0.369 |
None of the three conditions differ significantly from the expected value.
| No | Yes | |
|---|---|---|
| EX 50-50 | 12 | 37 |
| EX 80-20 | 8 | 49 |
| EX 20-80 | 7 | 48 |
\(\chi^2(2) = 3.04, p = 0.219, \varphi_c = 0.14\)
| No | Yes | |
|---|---|---|
| EX 50-50 | 1.73 | -1.73 |
| EX 80-20 | -0.69 | 0.69 |
| EX 20-80 | -0.99 | 0.99 |
| No | Yes | |
|---|---|---|
| EX 50-50 | 0.083 | 0.083 |
| EX 80-20 | 0.492 | 0.492 |
| EX 20-80 | 0.323 | 0.323 |
| value | comparison | odds_ratio | p_value | CI_low | CI_upper | p_value_adj |
|---|---|---|---|---|---|---|
| High | EX 50-50 : EX 80-20 | 0.9799 | 1.0000 | 0.3521 | 2.6883 | 1.0000 |
| High | EX 50-50 : EX 20-80 | 0.7080 | 0.5056 | 0.2603 | 1.8687 | 1.0000 |
| High | EX 80-20 : EX 20-80 | 0.7223 | 0.5201 | 0.2805 | 1.8310 | 1.0000 |
| Low | EX 50-50 : EX 80-20 | 1.9735 | 0.2157 | 0.6633 | 6.1822 | 1.0000 |
| Low | EX 50-50 : EX 20-80 | 2.2068 | 0.1357 | 0.7174 | 7.3155 | 0.8141 |
| Low | EX 80-20 : EX 20-80 | 1.1184 | 1.0000 | 0.3256 | 3.9337 | 1.0000 |
Note:
In the contingency tables, ‘Yes’ indicates the extreme value was recalled, ‘No’ indicates that it was not.
Only recalled outcomes that matched the programmed values were included. i.e., if they saw the High Value Risky Door, 80 was logged as “Yes” and 40 was logged as “No.” If they saw the Low Value Risky Door, 0 was logged as “Yes”, 40 was logged as “No”. Participants who responded with any “other” values were removed from the analysis. Only Risky doors were evaluated.
In total, removing “other” responses resulted 15 participants being excluded from these analyses leaving a final N = 161.
\(\varphi_c\) is Cramér’s V, a measure of association for two nominal variables (i.e., an effect size of sorts). It can take a value between 0 and 1, with 0 indicating no association (i.e., full independence).
Post-hoc analysis on each \(\chi^2\) test was conducted by evaluating
the standardized residuals from the chi-square analysis because it
seemed the most intuitive approach. However, pairwise Pearson
Chi-squared or Fisher Exact tests across the three conditions were also
run. The p_value_adj column shows corrected p-values using
the Holm-Bonferroni method.
| value | outcome | group | n | mean | sd | median | IQR |
|---|---|---|---|---|---|---|---|
| High | +40 | EX 50-50 | 58 | 42.897 | 17.085 | 50 | 10.00 |
| High | +40 | EX 80-20 | 64 | 43.094 | 18.564 | 50 | 20.00 |
| High | +40 | EX 20-80 | 62 | 43.516 | 20.001 | 50 | 30.00 |
| High | +80 | EX 50-50 | 58 | 49.966 | 16.012 | 50 | 8.75 |
| High | +80 | EX 80-20 | 64 | 52.672 | 20.788 | 50 | 15.25 |
| High | +80 | EX 20-80 | 62 | 50.210 | 17.479 | 50 | 20.00 |
| Low | 0 | EX 50-50 | 58 | 62.017 | 17.046 | 60 | 28.75 |
| Low | 0 | EX 80-20 | 64 | 60.219 | 23.109 | 60 | 26.25 |
| Low | 0 | EX 20-80 | 62 | 60.968 | 18.313 | 60 | 28.75 |
| Low | +40 | EX 50-50 | 58 | 32.466 | 17.017 | 30 | 30.00 |
| Low | +40 | EX 80-20 | 64 | 33.875 | 20.408 | 35 | 30.00 |
| Low | +40 | EX 20-80 | 62 | 32.410 | 19.266 | 33 | 30.00 |
| Model | df | AIC | BIC | logLik | Test | L.Ratio | p.value | BF_10 | |
|---|---|---|---|---|---|---|---|---|---|
| base | 1 | 4 | 3240.858 | 3256.490 | -1616.429 | NA | NA | NA | |
| cond_mod | 2 | 6 | 3244.737 | 3268.185 | -1616.368 | 1 vs 2 | 0.121 | 0.941 | 0.003 |
| HL_mod | 3 | 7 | 3221.010 | 3248.366 | -1603.505 | 2 vs 3 | 25.727 | 0.000 | 20117.182 |
| int_mod | 4 | 9 | 3224.021 | 3259.194 | -1603.010 | 3 vs 4 | 0.989 | 0.610 | 0.004 |
Main Effect of Condition:
\(\chi^2(2) = 0.12\), \(p = 0.941\), \(BF_{10} < .01\)
Main Effect of Value (High vs. Low):
\(\chi^2(1) = 25.73\), \(p < 0.001\), \(BF_{10} > 150\)
Interaction:
\(\chi^2(2) = 0.99\), \(p = 0.61\), \(BF_{10} < .01\)
| Value | Std.Error | DF | t-value | p-value | r_effect | |
|---|---|---|---|---|---|---|
| (Intercept) | 55.991 | 1.819 | 181 | 30.778 | 0.000 | 0.916 |
| group 8020_vs_50 | 0.454 | 2.512 | 181 | 0.181 | 0.857 | 0.013 |
| group 2080_vs_50 | -0.403 | 2.531 | 181 | -0.159 | 0.874 | 0.012 |
| fj_value1 | -6.026 | 1.714 | 181 | -3.517 | 0.001 | 0.253 |
| group 8020_vs_50 :fj_value1 | 2.252 | 2.366 | 181 | 0.952 | 0.342 | 0.071 |
| group 2080_vs_50 :fj_value1 | 0.647 | 2.384 | 181 | 0.271 | 0.786 | 0.020 |
EX 80-20 vs. EX 50:
\(b = 0.454\), \(t(181) = 0.18\), \(p = 0.857\), \(r = 0.013\)
EX 20-80 vs. EX 50:
\(b = -0.403\), \(t(181) = -0.16\), \(p = 0.874\), \(r = 0.012\)
EX 80-20 vs. EX 50 | Value (High vs. Low):
\(b = 2.252\), \(t(181) = 0.95\), \(p = 0.342\), \(r = 0.071\)
EX 20-80 vs. EX 50 | Value (High vs. Low):
\(b = 0.647\), \(t(181) = 0.27\), \(p = 0.786\), \(r = 0.02\)
ANOVA was conducted only on judgements for the risky extreme values (0 and +80).
Bayes Factors are reported as Inverse Bayes Factors, this means larger values indicate greater support for the effect. Anything less than 1 should be considered as contributing no evidence.
N = 190
| group | gender | n | age_mean | age_sd | age_median | age_IQR |
|---|---|---|---|---|---|---|
| BEST 50-50 | F | 50 | 19.220 | 3.699 | 18.5 | 1 |
| BEST 50-50 | M | 16 | 19.375 | 1.544 | 19.0 | 2 |
| BEST 80-20 | F | 48 | 19.500 | 3.156 | 18.0 | 1 |
| BEST 80-20 | M | 13 | 19.231 | 1.787 | 19.0 | 1 |
| BEST 20-80 | F | 38 | 18.842 | 1.636 | 18.0 | 1 |
| BEST 20-80 | M | 25 | 19.840 | 1.748 | 19.0 | 2 |
N = 183
| group | gender | n | age_mean | age_sd | age_median | age_IQR |
|---|---|---|---|---|---|---|
| BEST 50-50 | F | 46 | 19.326 | 3.842 | 19 | 1 |
| BEST 50-50 | M | 15 | 19.467 | 1.552 | 19 | 2 |
| BEST 80-20 | F | 48 | 19.500 | 3.156 | 18 | 1 |
| BEST 80-20 | M | 13 | 19.231 | 1.787 | 19 | 1 |
| BEST 20-80 | F | 36 | 18.889 | 1.670 | 18 | 1 |
| BEST 20-80 | M | 25 | 19.840 | 1.748 | 19 | 2 |
| group | n | age_mean | age_sd | age_median | age_IQR |
|---|---|---|---|---|---|
| BEST 50-50 | 61 | 19.361 | 3.411 | 19 | 1 |
| BEST 80-20 | 61 | 19.443 | 2.907 | 18 | 1 |
| BEST 20-80 | 61 | 19.279 | 1.752 | 19 | 2 |
Total number of catch trial exclusions = 7.
Catch trial exclusions were based on block 5 and 6 performance.
| Model | df | AIC | BIC | logLik | Test | L.Ratio | p.value | BF_10 | |
|---|---|---|---|---|---|---|---|---|---|
| base_mod | 1 | 4 | 247.353 | 262.964 | -119.677 | NA | NA | NA | |
| grp_mod | 2 | 6 | 249.708 | 273.124 | -118.854 | 1 vs 2 | 1.645 | 0.439 | 6.000000e-03 |
| value_mod | 3 | 7 | 157.116 | 184.435 | -71.558 | 2 vs 3 | 94.592 | 0.000 | 1.813658e+19 |
| grp_val | 4 | 9 | 153.345 | 188.469 | -67.673 | 3 vs 4 | 7.771 | 0.021 | 1.330000e-01 |
Main Effect of Group:
\(\chi^2(2) = 1.65, p = 0.439, BF_{10} < .01\)
Main Effect of Choice Value (i.e., Extreme Outcome effect):
\(\chi^2(1) = 94.59, p < .001, BF_{10} > 150\)
Interaction: Group \(\times\) Choice Value:
\(\chi^2(2) = 7.77, p = 0.021, BF_{10} = 0.133\)
| Value | Std.Error | DF | t-value | p-value | sig | r_effect | |
|---|---|---|---|---|---|---|---|
| (Intercept) | 0.383 | 0.033 | 180 | 11.747 | 0.000 | TRUE | 0.659 |
| group 8020_vs_50 | 0.024 | 0.046 | 180 | 0.511 | 0.610 | FALSE | 0.038 |
| group 2080_vs_50 | 0.058 | 0.046 | 180 | 1.267 | 0.207 | FALSE | 0.094 |
| choice_value1 | 0.159 | 0.022 | 180 | 7.329 | 0.000 | TRUE | 0.479 |
| group 8020_vs_50 :choice_value1 | 0.013 | 0.031 | 180 | 0.435 | 0.664 | FALSE | 0.032 |
| group 2080_vs_50 :choice_value1 | -0.067 | 0.031 | 180 | -2.173 | 0.031 | TRUE | 0.160 |
BEST 80-20 vs. BEST 50:
\(b = 0.02, t(180) = 0.51, p = 0.61, r = 0.04\)
BEST 20-80 vs. BEST 50:
\(b = 0.06, t(180) = 1.27, p = 0.207, r = 0.09\)
BEST 80-20 vs. BEST 50 | Choice Value (High vs. Low):
\(b = 0.01, t(180) = 0.43, p = 0.664, r = 0.03\)
BEST 20-80 vs. BEST 50 | Choice Value (High vs. Low):
\(b = -0.07, t(180) = -2.17, p = 0.031, r = 0.16\)
Note:
Proportions are taken within condition and context (High/Low). E.g., All the green bars in the top left sum to 1, all the orange bars in the top middle sum to 1, and so on.
Since non-numeric responses were permissible by the experiment’s program, data was filtered to remove all non-numeric inputs. If a participant’s inputs had a cumulative sum less than 20 or greater than 300, their results were removed. In total, 6 participants met this criteria.
| No | Yes | |
|---|---|---|
| BEST 50-50 | 15 | 43 |
| BEST 80-20 | 10 | 47 |
| BEST 20-80 | 23 | 30 |
\(\chi^2(2) = 9.31, p = 0.01, \varphi_c = 0.24\)
| No | Yes | |
|---|---|---|
| BEST 50-50 | -0.56 | 0.56 |
| BEST 80-20 | -2.27 | 2.27 |
| BEST 20-80 | 2.89 | -2.89 |
| No | Yes | |
|---|---|---|
| BEST 50-50 | 0.572 | 0.572 |
| BEST 80-20 | 0.023 | 0.023 |
| BEST 20-80 | 0.004 | 0.004 |
The BEST 80-20 and BEST 20-80 conditions both differ significantly from the expected value. The BEST 80-20 condition tends to recall the extreme value, whereas BEST 20-80 does not.
BEST 80-20: \(z = 2.27, p = 0.023\)
BEST 20-80: \(z = -2.89, p = 0.004\)
| No | Yes | |
|---|---|---|
| BEST 50-50 | 5 | 53 |
| BEST 80-20 | 12 | 45 |
| BEST 20-80 | 7 | 46 |
\(\chi^2(2) = 3.7, p = 0.157, \varphi_c = 0.15\)
| No | Yes | |
|---|---|---|
| BEST 50-50 | -1.52 | 1.52 |
| BEST 80-20 | 1.80 | -1.80 |
| BEST 20-80 | -0.27 | 0.27 |
| No | Yes | |
|---|---|---|
| BEST 50-50 | 0.128 | 0.128 |
| BEST 80-20 | 0.072 | 0.072 |
| BEST 20-80 | 0.786 | 0.786 |
| value | comparison | odds_ratio | p_value | CI_low | CI_upper | p_value_adj |
|---|---|---|---|---|---|---|
| High | BEST 50-50 : BEST 80-20 | 1.6325 | 0.3667 | 0.6105 | 4.5340 | 0.9612 |
| High | BEST 50-50 : BEST 20-80 | 0.4583 | 0.0713 | 0.1883 | 1.0884 | 0.3526 |
| High | BEST 80-20 : BEST 20-80 | 0.2809 | 0.0037 | 0.1037 | 0.7154 | 0.0223 |
| Low | BEST 50-50 : BEST 80-20 | 0.3569 | 0.0705 | 0.0914 | 1.1908 | 0.3526 |
| Low | BEST 50-50 : BEST 20-80 | 0.6226 | 0.5456 | 0.1453 | 2.4571 | 0.9612 |
| Low | BEST 80-20 : BEST 20-80 | 1.7435 | 0.3204 | 0.5713 | 5.7317 | 0.9612 |
Note:
In the contingency tables, ‘Yes’ indicates the extreme value was recalled, ‘No’ indicates that it was not.
Only recalled outcomes that matched the programmed values were included. i.e., if they saw the High Value Risky Door, 80 was logged as “Yes” and 40 was logged as “No.” If they saw the Low Value Risky Door, 0 was logged as “Yes”, 40 was logged as “No”. Participants who responded with any “other” values were removed from the analysis. Only Risky doors were evaluated.
In total, removing “other” responses resulted 9 participants being excluded from these analyses leaving a final N = 168.
\(\varphi_c\) is Cramér’s V, a measure of association for two nominal variables (i.e., an effect size of sorts). It can take a value between 0 and 1, with 0 indicating no association (i.e., full independence).
Post-hoc analysis on each \(\chi^2\) test was conducted by evaluating
the standardized residuals from the chi-square analysis because it
seemed the most intuitive approach. However, pairwise Pearson
Chi-squared or Fisher Exact tests across the three conditions were also
run. The p_value_adj column shows corrected p-values using
the Holm-Bonferroni method.
| value | outcome | group | n | mean | sd | median | IQR |
|---|---|---|---|---|---|---|---|
| High | +40 | BEST 50-50 | 61 | 39.344 | 20.886 | 40 | 30 |
| High | +40 | BEST 80-20 | 61 | 45.000 | 15.028 | 50 | 10 |
| High | +40 | BEST 20-80 | 61 | 49.770 | 21.064 | 50 | 30 |
| High | +80 | BEST 50-50 | 61 | 51.934 | 17.905 | 50 | 20 |
| High | +80 | BEST 80-20 | 61 | 50.492 | 12.573 | 50 | 20 |
| High | +80 | BEST 20-80 | 61 | 43.705 | 18.557 | 50 | 20 |
| Low | 0 | BEST 50-50 | 61 | 67.623 | 16.447 | 70 | 30 |
| Low | 0 | BEST 80-20 | 61 | 63.770 | 18.988 | 60 | 30 |
| Low | 0 | BEST 20-80 | 61 | 61.967 | 19.880 | 60 | 30 |
| Low | +40 | BEST 50-50 | 61 | 25.000 | 17.442 | 20 | 30 |
| Low | +40 | BEST 80-20 | 61 | 30.881 | 18.111 | 30 | 30 |
| Low | +40 | BEST 20-80 | 61 | 32.377 | 18.203 | 30 | 30 |
| Model | df | AIC | BIC | logLik | Test | L.Ratio | p.value | BF_10 | |
|---|---|---|---|---|---|---|---|---|---|
| base | 1 | 4 | 3215.285 | 3230.896 | -1603.643 | NA | NA | NA | |
| cond_mod | 2 | 6 | 3211.195 | 3234.611 | -1599.598 | 1 vs 2 | 8.090 | 0.018 | 1.560000e-01 |
| HL_mod | 3 | 7 | 3145.344 | 3172.662 | -1565.672 | 2 vs 3 | 67.851 | 0.000 | 2.831444e+13 |
| int_mod | 4 | 9 | 3148.096 | 3183.220 | -1565.048 | 3 vs 4 | 1.248 | 0.536 | 5.000000e-03 |
Main Effect of Condition:
\(\chi^2(2) = 8.09\), \(p = 0.018\), \(BF_{10} = 0.156\)
Main Effect of Value (High vs. Low):
\(\chi^2(1) = 67.85\), \(p < 0.001\), \(BF_{10} > 150\)
Interaction:
\(\chi^2(2) = 1.25\), \(p = 0.536\), \(BF_{10} < .01\)
| Value | Std.Error | DF | t-value | p-value | r_effect | |
|---|---|---|---|---|---|---|
| (Intercept) | 59.779 | 1.589 | 180 | 37.609 | 0.000 | 0.942 |
| group 8020_vs_50 | -2.648 | 2.248 | 180 | -1.178 | 0.240 | 0.087 |
| group 2080_vs_50 | -6.943 | 2.248 | 180 | -3.089 | 0.002 | 0.224 |
| fj_value1 | -7.844 | 1.589 | 180 | -4.935 | 0.000 | 0.345 |
| group 8020_vs_50 :fj_value1 | 1.205 | 2.248 | 180 | 0.536 | 0.593 | 0.040 |
| group 2080_vs_50 :fj_value1 | -1.287 | 2.248 | 180 | -0.572 | 0.568 | 0.043 |
BEST 80-20 vs. BEST 50:
\(b = -2.648\), \(t(180) = -1.18\), \(p = 0.24\), \(r = 0.087\)
BEST 20-80 vs. BEST 50:
\(b = -6.943\), \(t(180) = -3.09\), \(p = 0.002\), \(r = 0.224\)
BEST 80-20 vs. BEST 50 | Value (High vs. Low):
\(b = 1.205\), \(t(180) = 0.54\), \(p = 0.593\), \(r = 0.04\)
BEST 20-80 vs. BEST 50 | Value (High vs. Low):
\(b = -1.287\), \(t(180) = -0.57\), \(p = 0.568\), \(r = 0.043\)
ANOVA was conducted only on judgements for the risky extreme values (0 and +80).
Bayes Factors are reported as Inverse Bayes Factors, this means larger values indicate greater support for the effect. Anything less than 1 should be considered as contributing no evidence.
R version 4.4.2 (2024-10-31 ucrt)